
Average accuracy: the accuracy is averaged over all severity levels and corruptions:
\(\text{Accuracy}_f = 1 - \frac{1}{15 \cdot 5}\sum _{c=1}^{15} \sum _{s=1}^{5} E_{s,c}^{f}.\) 

Mean corruption error (mCE, proposed in [1]}): the error rate on each corruption is normalized by the error rate, \(E_{s,c}^{\text{AlexNet}}\) , of the standard deep learning model, AlexNet [2]}:
\(\text{mCE}_f = \frac{1}{15}\sum _{c=1}^{15} \frac{\sum _{s=1}^{5} E_{s,c}^{f}}{\sum _{s=1}^{5} E_{s,c}^{\text{AlexNet}}}.\) 
The motivation is to make the error rates on different corruptions more comparable. Indeed they do not all have the same inherent level of difficulty.

Relative mean corruption error (relative mCE, proposed in [1]}): instead of measuring the error rate, one can also consider the degradation of the error rate compared to the standard error rate \(E_{\text{standard}}^{f}\)  of the model \(f\)  taken relative to the degradation of the error rate \(E_{\text{standard}}^{\text{AlexNet}}\)  of AlexNet:
\(\text{Relative mCE}_f = \frac{1}{15}\sum _{c=1}^{15} \frac{\sum _{s=1}^{5} E_{s,c}^{f} - E_{\text{standard}}^{f}}{\sum _{s=1}^{5} E_{s,c}^{\text{AlexNet}} - E_{\text{standard}}^{\text{AlexNet}}}.\) 
However, this metric has to be carefully interpreted since it does not take absolute accuracy into account, e.g., a constant model achieves the perfect score of 0 for this metric.

